How do you find the derivative of f(x)=ax+b?

1 Answer
Sep 25, 2017

f^'(x)=a

Explanation:

f(x)=ax+b

Take derivative on both sides:

d/dx(f(x))=d/dx(ax+b)

Apply the sum/difference rule for derivative which is stated as:

d/dx(f+g)=d/dx(f)+d/dx(g)

So that we will have:

f^'(x)=d/dx(ax)+d/dx(b)

Remember the derivative of a constant is zero, so that we will have:

f^'(x)=d/dx(ax)+0

Take the constant out by applying d/dx(a*f)=a*d/dx(f)

f^'(x)=a*d/dx(x)

Apply the common derivative rule d/dx(x)=1

f^'(x)=a*1

f^'(x)=a